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Making an open statement to satisfy two conditions help!

  1. Mar 22, 2005 #1

    MtX

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    Hello guys,

    I have a question regarding mathematical logic that I'm stuck on. Here it is:

    T = { (5,9), (4,9), (5,7), (6,5), (5,5), (6,3), (7,1), (6,1), (5,1), (4,1), (3,1), (2,1), (1,1), (0,1) }
    F = { (5,4), (6,8 ), (2,11), (4,13), (8,1), (1,0) }

    1) Make a simple open statement P(x,y) so (x,y) in T -> P(x,y) and (x,y) in F -> !P(x,y). Use only domain N, comparison operators (<, =, >), operations (+, -) and logical notation and don't use T or F in P.

    2) Find an example (x,y) !in T so that P(x,y) and an example (x,y) !in F so that !P(x,y).

    My thoughts:

    1) I can't think of any general equation or formula so that T is true and F is false, but using cases I may be able to find something. Don't think I can use cases though because there's just too many... Next thing I did was look for patterns but I can't seem to find anything different from T and F. For T, 2x+y <= 19 and x+y <= 14 and -5 <= x-y <= 6 for all sets in T, but when we look at the sets in F, some of those sets satisfy the equations from T.. basically, NOT all of the sets in F are false, some are true.. what can i do to ensure all sets in T are true and all sets in F are false?

    2) ???
     
  2. jcsd
  3. Mar 22, 2005 #2
    My 2 cents :
    1>
    find the equation of the line that passes through all the points in T but not through any point in F.Let this function be f(x,y)
    P(x,y) : (x,y) is a point in f(x,y)

    -- AI
     
  4. Mar 22, 2005 #3
    Well, I don't know how simple your statement has to be but you could separate the points by regions (graphing them would help). You'd probably have to use five or six lines.
     
  5. Mar 22, 2005 #4

    MtX

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    im not sure what you mean by graphing them.. i put all the coordinates on a x/y graph, connected them with a line..
     
  6. Mar 22, 2005 #5

    MtX

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    after connecting all the sets of coordinates of T with a line, the line isnt even straight.. cant find the slope..
     
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